As an attempt to investigate the torsional-longitudinal vibrations of marine propeller shafting systems, this paper develops an integrated mathematical formulation to consider different aspects of the problem as clearly as possible. The previous works in this field mostly deal with the lumped-parameter or finite element simulations of the propeller and the main shaft while this paper employs a non-FEM distributed-parameter modeling. The Newton–Euler method is used to derive dynamic equations of the cantilever blading and the rotating main shaft. The lumped effects on the main shaft such as the thrust block, the rigid coupling and the propeller loadings are considered together with the variation of cross section and pretwist angle along the blades. Galerkin method is used to discretize the equations and find the lowest number of dominant modes for each degree of freedom. The coupling effect is then explained by classifying the mode shapes into three groups. It is found that taking blade deformations into account is advantageous to the vibration analysis of the problem.

为了研究船用螺旋桨轴系的扭转-纵向振动，本文提出了一种综合数学公式，以尽可能清晰地考虑问题的各个方面。该领域的先前工作主要涉及螺旋桨和主轴的集总参数或有限元模拟，而本文采用非FEM分布参数建模。牛顿-欧拉方法用于导出悬臂叶片和旋转主轴的动力学方程。考虑到主轴上的集总效应，例如推力块，刚性联轴器和螺旋桨负载，以及沿叶片的横截面和预绕角的变化。Galerkin方法用于离散方程式，并为每个自由度找到最少数量的主导模。然后通过将模式形状分为三组来说明耦合效果。发现，考虑叶片变形有利于问题的振动分析。